Mathematics Commons^™

New Examples Of Self-Dual Near-Extremal Ternary Codes Of Length 48 Derived From 2-(47,23,11) Designs, Sanja Rukavina, Vladimir Tonchev

Michigan Tech Publications, Part 2

In a recent paper (Araya and Harada, 2023), Araya and Harada gave examples of self-dual near-extremal ternary codes of length 48 for 145 distinct values of the number A12 of codewords of minimum weight 12, and raised the question about the existence of codes for other values of A12. In this note, we use symmetric 2-(47,23,11) designs with an automorphism group of order 6 to construct self-dual near-extremal ternary codes of length 48 for 150 new values of A12.

Parabolic And Non-Parabolic Surfaces With Small Or Large End Spaces Via Fenchel-Nielsen Parameters, Michael Antony Pandazis

Dissertations, Theses, and Capstone Projects

We consider conditions on the Fenchel-Nielsen parameters of a Riemann surface X that determine whether or not a surface X is parabolic. Fix a geodesic pants decomposition of a surface and call the boundary geodesics in the decomposition cuffs. For a zero or half-twist flute surface, we prove that parabolicity is equivalent to the surface having a covering group of the first kind. Using that result, we give necessary and sufficient conditions on the Fenchel-Nielsen parameters of a half-twist flute surface X with increasing cuff lengths such that X is parabolic. As an application, we determine whether or not each …

Higher Diffeology Theory, Emilio Minichiello

Dissertations, Theses, and Capstone Projects

Finite dimensional smooth manifolds have been studied for hundreds of years, and a massive theory has been built around them. However, modern mathematicians and physicists are commonly dealing with objects outside the purview of classical differential geometry, such as orbifolds and loop spaces. Diffeology is a new framework for dealing with such generalized smooth spaces. This theory (whose development started in earnest in the 1980s) has started to catch on amongst the wider mathematical community, thanks to its simplicity and power, but it is not the only approach to dealing with generalized smooth spaces. Higher topos theory is another such …

Bifurcations And Resultants For Rational Maps And Dynatomic Modular Curves In Positive Characteristic, Colette Lapointe

Dissertations, Theses, and Capstone Projects

No abstract provided.

Sigma_N-Correct Forcing Axioms, Benjamin P. Goodman

Dissertations, Theses, and Capstone Projects

I introduce a new family of axioms extending ZFC set theory, the Sigma_n-correct forcing axioms. These assert roughly that whenever a forcing name a' can be forced by a poset in some forcing class Gamma to have some Sigma_n property phi which is provably preserved by all further forcing in Gamma, then a' reflects to some small name such that there is already in V a filter which interprets that small name so that phi holds. Sigma_1-correct forcing axioms turn out to be equivalent to classical forcing axioms, while Sigma_2-correct forcing axioms for Sigma_2-definable forcing classes are consistent relative to …

Explicit Composition Identities For Higher Composition Laws In The Quadratic Case, Ajith A. Nair

Dissertations, Theses, and Capstone Projects

The theory of Gauss composition of integer binary quadratic forms provides a very useful way to compute the structure of ideal class groups in quadratic number fields. In addition to that, Gauss composition is also important in the problem of representations of integers by binary quadratic forms. In 2001, Bhargava discovered a new approach to Gauss composition which uses 2x2x2 integer cubes, and he proved a composition law for such cubes. Furthermore, from the higher composition law on cubes, he derived four new higher composition laws on the following spaces - 1) binary cubic forms, 2) pairs of binary quadratic …

Me And Mathematics: “Doing What You’Re Talking About”: In Dialogue With My Family, Eden Morris

Dissertations, Theses, and Capstone Projects

This paper is a philosophically oriented accompaniment to my audio project (accessible through the following link: https://cuny.manifoldapp.org/projects/me-and-mathematics). Working together, the paper and audio collages form a call to action and a resource. My primary finding is the importance of doing what you’re talking about or exploring and implementing your ideas experientially. Doing what you’re talking about is important for effective teaching/learning and feeling in line with oneself. This working concept came to my attention during my research conversation with my oldest living relative, and then, again, with my youngest (non-baby) relative. This doing what you’re talking about is a way …

Differential Equations For Modeling Pathways Leading To Diabetes Onset, Viktoria Savatorova, Aleksei Talonov

CODEE Journal

This paper presents a mathematical model that explains potential pathways leading to diabetes onset. By utilizing a system of nonlinear differential equations to describe the dynamics of the glucose regulatory system, the model can serve as a pedagogical tool for teaching and learning differential equations, dynamical systems, mathematical modeling, and introduction to biomathematics. Within this framework, students can analyze equilibrium solutions, investigate stability, assess parameter sensitivity, and explore the potential for bifurcations. Theoretical analysis is complemented by illustrative numerical examples. Instructors have the flexibility to adapt and incorporate suggested activities according to their teaching preferences and objectives.

Weakly Pseudo Primary 2-Absorbing Submodules, Omar Hisham Taha, Marrwa Abdulla Salih

Al-Bahir Journal for Engineering and Pure Sciences

Let be a commutative ring with identity. In this paper, we introduce the notion of a weakly pseudo primary 2-absorbing sub-module as a generalization of a 2-absorbing sub-module and a pseudo 2-absorbing sub-module. Moreover, we give many basic properties, examples, and characterizations of these notions.

Constructible Sandwich Cut, Philip A. Son

FIU Undergraduate Research Journal

In mathematical measure theory, the “Ham-Sandwich” theorem states that any n objects in an n-dimensional Euclidean space can be simultaneously divided in half with a single cut by an (n-1)-dimensional hyperplane. While it guarantees its existence, the theorem does not provide a way of finding this halving hyperplane, as it is only an existence result. In this paper, we look at the problem in dimension 2, more in the style of Euclid and the antique Greeks, that is from a constructible point of view, with straight edge and compass. For two arbitrary regions in the plane, there is certainly no …

Canonical Extensions Of Quantale Enriched Categories, Alexander Kurz

MPP Research Seminar

No abstract provided.

A Mceliece Cryptosystem, Using Permutation Error-Correcting Codes, Fiona Smith

CSB and SJU Distinguished Thesis

Using existing methods of cryptography, we can encrypt messages through the internet. However, these methods are vulnerable to attacks done by a quantum computer, which are a rising threat to security. In this thesis I discuss a possible method of encryption, secure against quantum attacks, using permutation groups and coding theory.

Representations Of Gender In Math-Related Films, Jacob Gathje

CSB and SJU Distinguished Thesis

This project analyzes how four popular math-related films - Hidden Figures, Mean Girls, Good Will Hunting, and A Beautiful Mind - either follow, resist, or reconfigure gender stereotypes in mathematics. It includes close readings of specific scenes in each of the films, along with broader analysis of the effects of how women and men are represented differently. It concludes forward-looking focus, providing suggestions for how future math-related movies can depict a more realistic and inclusive version of the field of mathematics. Ideally, this will help improve one part of the larger issue of gender disparities in math.

Calculations From On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels

Mathematics and Statistics Student Research and Class Projects

In the field of nonlinear waves, particular interest is given to periodic traveling-wave solutions of nonlinear, dispersive wave equations. This thesis aims to determine the existence of periodic traveling-wave solutions for several systems of water wave equations. These systems are the Schr¨odinger KdV-KdV, Schr¨odinger BBM-BBM, Schr¨odinger KdV-BBM, and Schr¨odinger BBM-KdV systems, and the abcd-system. In particular, it is shown that periodic traveling-wave solutions exist and are explicitly given in terms of cnoidal, the Jacobi elliptic function. Certain solitary-wave solutions are also established as a limiting case of the periodic traveling-wave solutions, that is, as the elliptic modulus approaches one.

Boolean Group Structure In Class Groups Of Positive Definite Quadratic Forms Of Primitive Discriminant, Christopher Albert Hudert Jr.

Student Research Submissions

It is possible to completely describe the representation of any integer by binary quadratic forms of a given discriminant when the discriminant’s class group is a Boolean group (also known as an elementary abelian 2-group). For other discriminants, we can partially describe the representation using the structure of the class group. The goal of the present project is to find whether any class group with 32 elements and a primitive positive definite discriminant is a Boolean group. We find that no such class group is Boolean.

Approval Gap Of Weighted K-Majority Tournaments, Jeremy Coste, Breeann Flesch, Joshua D. Laison, Erin Mcnicholas, Dane Miyata

Theory and Applications of Graphs

A $k$-majority tournament $T$ on a finite set of vertices $V$ is defined by a set of $2k-1$ linear orders on $V$, with an edge $u \to v$ in $T$ if $u>v$ in a majority of the linear orders. We think of the linear orders as voter preferences and the vertices of $T$ as candidates, with an edge $u \to v$ in $T$ if a majority of voters prefer candidate $u$ to candidate $v$. In this paper we introduce weighted $k$-majority tournaments, with each edge $u \to v$ weighted by the number of voters preferring $u$.

We define the …

On Distortion Of Surface Groups In Right-Angled Artin Groups, Lucas Bridges

Mathematical Sciences Undergraduate Honors Theses

Surfaces have long been a topic of interest for scholars inside and outside of mathe- matics. In a topological sense, surfaces are spaces which appear flat on a local scale. Surfaces in this sense have a restricted set of properties, including the behavior of loops around a surface, codified in the fundamental group.

All but 3 surface groups have been shown to embed into a class of groups called right-angled Artin groups. The method through which these embeddings are created places large restrictions on all homomorphisms from surface groups to right-angled Artin groups.

One such restriction on these homomorphisms is …

Local Existence Of Solutions To A Nonlinear Autonomous Pde Model For Population Dynamics With Nonlocal Transport And Competition, Michael R. Lindstrom

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Highlights

• Partial differential equation models are ubiquitous in applied sciences.

• A partial differential equation based in ecology is studied for solution existence.

• Energy methods and convergence analysis lead to local classical solutions.

Abstract

In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to qualitatively describe temporal changes in population densities over space through accounting for location desirability and fast, long-range travel. Beginning with sufficiently regular initial conditions, through smoothing the PDE and employing energy arguments, we obtain a sequence …

Weighted Ehrhart Theory: Extending Stanley's Nonnegativity Theorem, Esme Bajo, Robert Davis, Jesús A. De Loera, Alexey Garber, Sofía Garzón Mora, Katharina Jochemko, Josephine Yu

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We generalize R. P. Stanley's celebrated theorem that the h∗-polynomial of the Ehrhart series of a rational polytope has nonnegative coefficients and is monotone under containment of polytopes. We show that these results continue to hold for weighted Ehrhart series where lattice points are counted with polynomial weights, as long as the weights are homogeneous polynomials decomposable as sums of products of linear forms that are nonnegative on the polytope. We also show nonnegativity of the h∗-polynomial as a real-valued function for a larger family of weights.

We generalize R. P. Stanley's celebrated theorem that the h ⁎ -polynomial of …

Modeling The Neutral Densities Of Sparc Using A Python Version Of Kn1d, Gwendolyn R. Galleher

Undergraduate Honors Theses

Currently, neutral recycling is a crucial contributor to fueling the plasma within tokamaks. However, Commonwealth Fusion System’s SPARC Tokamak is expected to be more opaque to neutrals. Thus, we anticipate that the role of neutral recycling in fueling will decrease. Since SPARC is predicted to have a groundbreaking fusion power gain ratio of Q ≈ 10, we must have a concrete understanding of the opacity
and whether or not alternative fueling practices must be included. To develop said understanding, we produced neutral density profiles via KN1DPy, a 1D kinetic neutral transport code for atomic and molecular hydrogen in an ionizing …